% 20061121 
%% Exempel 8.22 i Montgomerys bok
% (c) Jan Rohlén
% Exemplet skall illustrera EWMA

% Data

X=[
953
945
972
945
975
970
959
973
940
936
985
973
955
950
948
957
940
933
965
973
949
941
966
966
934
937
946
952
935
941
937
946
954
935
941
933
960
968
959
956
959
939
948
958
963
973
949
942
965
962
948
937
955
927
940
962
963
943
950
938
958
955
947
941
938
945
963
967
969
981
952
931
928
937
950
970
933
960
934
927
];


% Vi antar att
Mu0=950;
%Sigma0=std(X);
Sigma0=mean(abs(diff(X)))/1.128

%% Börjar med att rita ett Shewhartdiagram
close all hidden


%% Konstruera CUMSUM

K=0.5*Sigma0;
H=5*Sigma0;


CP=[0,0];

CM=[0,0];

for k=1: length(X)
    NP=CP(k,2);
    CP_new=max(0,X(k)-(Mu0+K)+CP(k,1));
    if CP_new>0
        NP=NP+1;
    else
        NP=0;
    end
    CP=[CP; CP_new , NP];
    
    NM=CM(k,2);
    CM_new=max(0,(Mu0-K)-X(k)+CM(k,1));
    if CM_new>0
        NM=NM+1;
    else
        NM=0;
    end
    CM=[CM; CM_new , NM];
        
%     CP=[CP,max(0,X(k)-(Mu0+K)+CP(length(CP)))];
%     CM=[CM,max(0,(Mu0-K)-X(k)+CM(length(CM)))];
end

figure
plot(CP(:,1),'o-k','MarkerFaceColor','b')
hold
plot(-CM(:,1),'o-k','MarkerFaceColor','g')


plot(find(CM(:,1)==-CP(:,1)),find(CM(:,1)==-CP(:,1))*0,'o','MarkerFaceColor','w')
plot(X*0+H*1,'r')
plot(X*0-H*1,'r')

ylabel('CumSum','FontSize',12)
xlabel('Provnummer','FontSize',12)
title('Ex. 8-1 Tabell-Cumsum','FontSize',18)
legend('Positiv CumSUM','Negativ CumSum')


%% Konstruera EWMA-plot
L=0.4;  % Parametern Lambda


z=Mu0;  % Initiera

for i=1: length(X)
    z=[z;L*X(i)+(1-L)*z(length(z))];
    UCL(i)=Mu0+ 3*sqrt(L/(2-L)*(1-(1-L).^(2*i)))*Sigma0;
    LCL(i)=Mu0- 3*sqrt(L/(2-L)*(1-(1-L).^(2*i)))*Sigma0;
    CL(i)=Mu0;
end
z(1)=[];

figure
hold

plot(z,'o-k','MarkerFaceColor','b')

k=(0.5:1:length(X))';
stairs(k,UCL,'r')
stairs(k,LCL,'r')
plot(CL,'r--')

title('Ex 8-1: EWMA styrdiagram, L=3.0 och \lambda=0.4','FontSize',18)